#P702E. Analysis of Pathes in Functional Graph
Analysis of Pathes in Functional Graph
Description
You are given a functional graph. It is a directed graph, in which from each vertex goes exactly one arc. The vertices are numerated from 0 to n - 1.
Graph is given as the array f0, f1, ..., fn - 1, where fi — the number of vertex to which goes the only arc from the vertex i. Besides you are given array with weights of the arcs w0, w1, ..., wn - 1, where wi — the arc weight from i to fi.
The graph from the first sample test. Also you are given the integer k (the length of the path) and you need to find for each vertex two numbers si and mi, where:
- si — the sum of the weights of all arcs of the path with length equals to k which starts from the vertex i;
- mi — the minimal weight from all arcs on the path with length k which starts from the vertex i.
The length of the path is the number of arcs on this path.
The first line contains two integers n, k (1 ≤ n ≤ 105, 1 ≤ k ≤ 1010). The second line contains the sequence f0, f1, ..., fn - 1 (0 ≤ fi < n) and the third — the sequence w0, w1, ..., wn - 1 (0 ≤ wi ≤ 108).
Print n lines, the pair of integers si, mi in each line.
Input
The first line contains two integers n, k (1 ≤ n ≤ 105, 1 ≤ k ≤ 1010). The second line contains the sequence f0, f1, ..., fn - 1 (0 ≤ fi < n) and the third — the sequence w0, w1, ..., wn - 1 (0 ≤ wi ≤ 108).
Output
Print n lines, the pair of integers si, mi in each line.
Samples
7 3
1 2 3 4 3 2 6
6 3 1 4 2 2 3
10 1
8 1
7 1
10 2
8 2
7 1
9 3
4 4
0 1 2 3
0 1 2 3
0 0
4 1
8 2
12 3
5 3
1 2 3 4 0
4 1 2 14 3
7 1
17 1
19 2
21 3
8 1